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Figure 1 - This figures shows…

Figure 1 - This figures shows…

Code

  1. R environment setup
  2. Setting time breaks
  3. Defining origins
  4. Import raster data
  5. GAM smoothing models
  6. Compare rates between origins and not-origins
  7. Compare rates between different time periods
  8. Setup final figure
  9. Map for final figure
  10. Trend through time panel for final figure
  11. Assemble and print final figure

R environment setup

Attach libraries

library(png)
library(maptools)
Checking rgeos availability: TRUE
library(raster)
library(gam)
Loading required package: splines
Loading required package: foreach
foreach: simple, scalable parallel programming from Revolution Analytics
Use Revolution R for scalability, fault tolerance and more.
http://www.revolutionanalytics.com
Loaded gam 1.14

Set working directory

setwd("~/Desktop/Botero postdoc 2016/Human density and the origins of agriculture/")

Setting time breaks

Define the times of agricultural origins

par(mar=c(0,0,0,20))
d <- readPNG("Larson_dates.png")
plot(seq(0,18, length.out = 19), seq(0,36, length.out = 19), type="n",ylim=c(0,36),xlim=c(0, 18), xaxt="n")
rasterImage(d, 0,0,18,36, interpolate=TRUE, col=d)
Start_of_early_window <- 16-12
End_of_early_window_start_of_late_window <- 8.2
End_of_late_window <- 17-4.2
polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(0, 34, 34, 0), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(0, 34, 34, 0), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

These dates are provided in the supplimentary information for the Larson (2014) paper. I’ve copied those values into a .csv table provided here.

domestication_times <- read.csv("Domestication timing larson 2014.csv")
dim(domestication_times)
[1] 77  8
Region Species Start.Exploitation Finish.Exploitation Start.predomestication Finish.predomestication Start.Domestication Finish.Domestication
Southwest asia Wheat 12.00 11.25 11.25 11.00 11.00 9.00
Southwest asia Barley 12.00 11.25 11.25 10.50 10.50 9.00
Southwest asia Lentil 12.00 11.00 11.00 10.50 10.50 9.00
Southwest asia Pea 11.50 11.00 11.00 10.00 10.00 8.50
Southwest asia Chickpea 11.00 10.50 10.50 10.25 10.25 8.25
Southwest asia Broadbean NA NA NA NA 10.50 NA
Southwest asia Flax 12.00 9.50 NA NA 9.50 NA
Southwest asia Olive 10.00 6.00 NA NA 6.00 NA
Southwest asia Sheep 12.00 10.50 10.50 9.75 9.75 8.00
Southwest asia Goat 12.00 10.50 10.50 9.75 9.75 8.00
Southwest asia Pig 12.00 11.50 11.50 9.75 10.25 9.00
Southwest asia Cattle, taurine 11.50 10.50 10.50 10.25 10.25 8.00
Southwest asia Cat NA NA 10.50 4.00 4.00 NA
South Asia Tree cotton 8.50 4.50 NA NA 4.50 NA
South Asia Rice 8.00 5.00 5.00 4.00 4.00 2.50
South Asia Little millet NA NA NA NA 4.50 NA
South Asia Browntop millet NA NA NA NA 4.00 NA
South Asia Mungbean NA NA 4.50 3.50 3.50 3.00
South Asia Pigeonpea NA NA NA NA 3.50 NA
South Asia Zebu cattle 9.00 8.00 NA NA 8.00 6.50
South Asia Water buffalo 6.00 4.50 NA NA 4.50 NA
East Asia Broomcorn Millet 10.00 8.00 NA NA 8.00 NA
East Asia Foxtail millet 11.50 7.50 NA NA 7.50 NA
East Asia Rice 10.00 8.00 8.00 7.50 7.50 5.00
East Asia Soybean 8.50 5.50 NA NA 5.50 4.00
East Asia Ramie NA NA NA NA 5.25 NA
East Asia Melon 7.00 4.00 NA NA 4.00 3.75
East Asia Pig 12.00 8.50 NA NA 8.50 6.00
East Asia Silkworm 7.00 5.25 NA NA 5.25 NA
East Asia Yak NA NA NA NA 4.25 NA
East Asia Horse 7.50 6.75 6.75 5.50 5.50 4.00
East Asia Bactrian Camel NA NA NA NA 4.50 NA
East Asia Duck 2.50 1.00 NA NA 1.00 NA
East Asia Chicken 6.00 4.00 NA NA 4.00 NA
New Guinea Banana 10.00 7.00 7.00 4.00 4.00 NA
New Guinea Taro 10.00 7.00 7.00 4.00 NA NA
New Guinea Yam 10.00 7.00 7.00 4.00 NA NA
Africa and Arabia Date palm 7.00 6.00 NA NA 5.00 NA
Africa and Arabia Sorghum 8.00 4.00 NA NA 4.00 NA
Africa and Arabia Pearl millet NA NA NA NA 4.50 3.50
Africa and Arabia Fonio NA NA NA NA 2.50 NA
Africa and Arabia Cowpea NA NA NA NA 3.75 NA
Africa and Arabia Hyacinth bean NA NA NA NA 3.75 NA
Africa and Arabia Rice 3.50 2.00 NA NA 2.00 NA
Africa and Arabia Oil palm 9.25 3.50 NA NA 3.50 NA
Africa and Arabia Cattle NA NA 9.00 7.75 7.75 6.50
Africa and Arabia Donkey 9.00 5.50 NA NA 5.50 3.50
Africa and Arabia Dromedary camel 6.50 3.00 NA NA 3.00 NA
Africa and Arabia Guinea fowl NA NA 2.50 1.50 1.50 NA
North America Squash 6.50 5.00 NA NA 5.00 NA
North America Sunflower 6.00 4.75 NA NA 4.00 NA
North America Sumpweed 6.00 4.50 NA NA 4.00 NA
North America Pitseed goosefoot 4.75 3.75 NA NA 3.75 NA
Meso-america Squash (pepo) NA NA NA NA 10.00 9.50
Meso-america Maize 10.00 9.00 NA NA 9.00 NA
Meso-america Foxtail millet-grass NA NA NA NA 6.00 4.00
Meso-america Common bean NA NA NA NA 3.00 NA
Meso-america Avocado NA NA NA NA 3.00 NA
Meso-america Chile pepper NA NA NA NA 3.00 NA
Meso-america Turkey NA NA NA NA 2.00 NA
South America Chili pepper NA NA NA NA 6.00 NA
South America Peanut NA NA NA NA 5.00 NA
South America Cotton NA NA NA NA 6.00 NA
South America Coca NA NA NA NA 8.00 NA
South America Now-minor root crops (arrowroot, leren) NA NA NA NA 9.00 NA
South America Squash NA NA NA NA 10.00 NA
South America Common bean NA NA NA NA 5.00 NA
South America Lima bean NA NA 8.25 NA 6.00 NA
South America Monioc NA NA NA NA 7.00 NA
South America Sweet potato NA NA NA NA 5.00 NA
South America White potato 7.00 4.50 NA NA 4.00 NA
South America Quinoa 5.00 NA NA NA 3.50 NA
South America Yam NA NA NA NA 5.50 NA
South America Llama 10.00 6.00 NA NA 6.00 NA
South America Alpaca 10.00 5.00 NA NA 5.00 NA
South America Guinea pig NA NA NA NA 5.00 NA
South America Muscovy Duck NA NA NA NA 4.00 NA
par(mar=c(5,4,6,1))
dates <- unlist(domestication_times[3:8])
hist(dates, breaks = 22, xlim=c(15,0), xlab="K years ago", col=adjustcolor("cornflowerblue", alpha= 0.5), border=adjustcolor("cornflowerblue", alpha= 0.9), main="All dates in dataset"  )
mtext("This tells us about how evenly our evidence is distributed in time", 3, line=1)

hist(dates, breaks = 22, xlim=c(15,0), xlab="Thousand years ago", col=adjustcolor("cornflowerblue", alpha= 0.5), border=adjustcolor("cornflowerblue", alpha= 0.9), main="All dates in dataset with Larson(2014) date windows")
Start_of_early_window <- 12
End_of_early_window_start_of_late_window <- 8.2
End_of_late_window <- 4.2
polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
hist(dates, breaks = 22, xlim=c(15,0), xlab="K years ago", col=adjustcolor("cornflowerblue", alpha= 0.2), border=adjustcolor("cornflowerblue", alpha= 0.9), main="", add=TRUE)
mtext("Early Holocene", 3, line = -1, adj=.3)
mtext("Middle Holocene", 3, line= -1, adj=.6)

par(mfrow=c(2,3), mar=c(4,4,2,0))
dim(domestication_times)
[1] 77  8
specific_dates <- domestication_times[,3:8]
for(i in c(1, 3, 5, 2, 4, 6)){
hist(specific_dates[,i], breaks = 22, xlim=c(15,0), xlab="Thousand years ago", col=adjustcolor("cornflowerblue", alpha= 0.5), border=adjustcolor("cornflowerblue", alpha= 0.9), main= names(specific_dates)[i])
Start_of_early_window <- 12
End_of_early_window_start_of_late_window <- 8.2
End_of_late_window <- 4.2
polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
hist(specific_dates[,i], breaks = 22, xlim=c(15,0), xlab="K years ago", col=adjustcolor("cornflowerblue", alpha= 0.2), border=adjustcolor("cornflowerblue", alpha= 0.9), main="", add=TRUE)
}

I’m creating new rows for this table, combining dates in different ways to make the CDFs below look more authentic. This makes it so that pre-ag always happens before post-ag. What I’ve done is given the later date to the earlier date when those dates are missing.

h <- which(is.na(domestication_times[,3]))
domestication_times <- cbind(domestication_times, rep(NA, length(domestication_times[,1])))
domestication_times[,9] <- domestication_times[,3]
domestication_times[h,9] <- domestication_times[h,7]
colnames(domestication_times)[9] <- "adopt exploitation date"
domestication_times[,10] <- domestication_times[,7]
domestication_times[which(is.na(domestication_times[,10])),10] <- 0
colnames(domestication_times)[10] <- "start of ag"
#save(domestication_times, file="~/Desktop/Human density and the origins of agriculture/Domestication timing larson 2014.Rdata")

I think these are best described by a cummulative distribution, showing how they accumulate over time.

for(i in 1:8){
type_number <- i
    match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
    maxer <- max(match, na.rm=TRUE)
    j <- ecdf(maxer-match)
    print(levels(domestication_times$Region)[ type_number])
    print(match)
    print(j)
}
[1] "Africa and Arabia"
 [1] 7.00 8.00 4.50 2.50 3.75 3.75 3.50 9.25 7.75 9.00 6.50 1.50
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,   0.25,   1.25,  ...,   6.75,   7.75
[1] "East Asia"
 [1] 10.00 11.50 10.00  8.50  5.25  7.00 12.00  7.00  4.25  7.50  4.50  2.50  6.00
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,    0.5,      2,  ...,   7.75,    9.5
[1] "Meso-america"
[1] 10 10  6  3  3  3  2
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:4] =      0,      4,      7,      8
[1] "New Guinea"
[1] 10 10 10
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:1] =      0
[1] "North America"
[1] 6.50 6.00 6.00 4.75
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:3] =      0,    0.5,   1.75
[1] "South America"
 [1]  6.0  5.0  6.0  8.0  9.0 10.0  5.0  6.0  7.0  5.0  7.0  5.0  5.5 10.0 10.0  5.0  4.0
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:8] =      0,      1,      2,  ...,      5,      6
[1] "South Asia"
[1] 8.5 8.0 4.5 4.0 3.5 3.5 9.0 6.0
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:7] =      0,    0.5,      1,  ...,      5,    5.5
[1] "Southwest asia"
 [1] 12.0 12.0 12.0 11.5 11.0 10.5 12.0 10.0 12.0 12.0 12.0 11.5  4.0
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:6] =      0,    0.5,      1,  ...,      2,      8
par(mfcol=c(2,5), mar=c(4,0,5,0))
plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)
plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)
for(i in 1:8){
type_number <- i
    match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
    maxer <- max(match, na.rm=TRUE)
    j <- ecdf(maxer-match)
    #print(j)
    
plot(0,0, xlim=c(15,0), ylim=c(0,100), ylab="Percent of species that will eventually \n be domesticated in a region", xlab="Thousand years ago", main=levels(domestication_times$Region)[ type_number], type="n", yaxt="n")
x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- 100 * (c(0, j(seq(0, maxer, length.out=100))))
lines(x_seq, y_seq,  ylim=c(-1,1))
polygon(c(0, x_seq), c(0, y_seq), border=adjustcolor("cornflowerblue",alpha=1), col=adjustcolor("cornflowerblue", alpha=0.2))
if(i == 2 | i == 1)axis(2)
if(i == 3)mtext("Cummulative distribution function for the accumulation of domesticates", 3, line=3.8, col="cornflowerblue")
}

par(mfcol=c(2,5), mar=c(4,0,5,0))
plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)
plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)
for(i in 1:8){
type_number <- i
    match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
    maxer <- max(match, na.rm=TRUE)
    j <- ecdf(maxer-match)
    #print(j)
    
plot(0,0, xlim=c(15,0), ylim=c(0,100), ylab="Percent of species that will eventually \n be domesticated in a region", xlab="Thousand years ago", main=levels(domestication_times$Region)[ type_number], type="n", yaxt="n")
x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- 100 * (c(0, j(seq(0, maxer, length.out=100))))
lines(x_seq, y_seq,  ylim=c(-1,1))
polygon(c(0, x_seq), c(0, y_seq), border=adjustcolor("cornflowerblue",alpha=1), col=adjustcolor("cornflowerblue", alpha=0.2))
abline(v= maxer - quantile(j)[2], col="limegreen", lwd=2)
if(i == 2 | i == 1)axis(2)
if(i == 2)mtext("25%", 3, line=3.5, adj=-1, col="limegreen")
if(i == 3)mtext("Cummulative distribution function for the accumulation of domesticates", 3, line=3.8, col="cornflowerblue")
if(i == 4)mtext("Choose a y to predict an x", 3, line=3.3, col="cornflowerblue")
    break_one <- maxer
            break_two <- maxer - quantile(j)[2]
                
    polygon(x=c(break_two, break_two, break_one, break_one), y=c(0, 1, 1, 0), col=adjustcolor("cornflowerblue", alpha=0.2), border=adjustcolor("cornflowerblue",alpha=1))
            lines(x=c(break_two, break_two), y=c(0,-1), col="cornflowerblue")
            abline(h = 25, col="limegreen", lwd=2)
}

Make this a function. There is a choice of two methods here. At the end of this section we need to print the desision we’re passing to the later analyses.

Defining origins

origins <- readShapePoly('Origins_updated.shp')
origin.time.region <- c(2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 
                        2, 2, 1, 2, 2, 2, 2, 2, 2, 2) # 1 = early; 2 = middle
as.character(origins$CONTINENT)
 [1] "W_African_Sav" "Sudanic_Savan" "West Africa T" "Ethipian plat" NA             
 [6] "E_North_Ameri" "New_Guinea"    "Mesoamerica"   "N_Lowland_SA"  "NW_Lowland_SA"
[11] "Sava_W_India"  "S_India"       "Ganges_E_Indi" "Chinese_loess" "Japanese"     
[16] "Lower-MiddleY" "South trop ch" NA              "Southwes amaz" "C/S_Andes"    
#subset_order <- c(1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 17, 18)
subset_order <- c(8, 10, 9, 5, 18, 7, 6, 20, 1, 2, 13, 16)
origins_subset <- origins[subset_order,]
origins_subset$CONTINENT
 [1] Mesoamerica   NW_Lowland_SA N_Lowland_SA  <NA>          <NA>          New_Guinea   
 [7] E_North_Ameri C/S_Andes     W_African_Sav Sudanic_Savan Ganges_E_Indi Lower-MiddleY
18 Levels: C/S_Andes Chinese_loess E_North_Ameri Ethipian plat Ganges_E_Indi ... West Africa T
origins_subset$name
NULL
library(maps)
map()
map(origins, add=TRUE, fill=TRUE, col=adjustcolor("cornflowerblue", alpha=1))
database does not (uniquely) contain the field 'name'.

map()
d <- readPNG("Larson_origins.png")
rasterImage(d, -180, -90, 180, 110, interpolate=TRUE, col=d)
map(add=TRUE)
map(origins, add=TRUE, fill=TRUE, col=adjustcolor("cornflowerblue", alpha=1))
database does not (uniquely) contain the field 'name'.

# need to reproject

This is obviously a bad projection fit right now.

Import raster data

#subset and reorder origins. This is currently done at the end of the plot but should be moved forward.
# Load data for population density
load("PopD_all_December.rdata")
PopD.ALL
class       : RasterStack 
dimensions  : 288, 720, 207360, 18  (nrow, ncol, ncell, nlayers)
resolution  : 0.5, 0.5  (x, y)
extent      : -180, 180, -60, 84  (xmin, xmax, ymin, ymax)
coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
names       :        fourK,        fiveK,         sixK,       sevenK,       eightK,        nineK,         tenK,      elevenK,      twelveK,    thirteenK,    fourteenK,     fifteenK,     sixteenK,   seventeenK,    eighteenK, ... 
min values  : 5.611358e-07, 1.067142e-06, 2.508241e-06, 6.317553e-06, 2.286934e-05, 7.631922e-05, 1.272693e-04, 2.118215e-04, 2.602175e-04, 3.226203e-04, 4.390267e-04, 5.572032e-04, 7.313966e-04, 8.286005e-04, 8.297062e-04, ... 
max values  :     2.051069,     2.013452,     2.142908,     1.888403,     1.863014,     1.880628,     1.650615,     1.678033,     1.697732,     1.499115,     1.517264,     1.443677,     1.464867,     1.453581,     1.436394, ... 
# Extract data to a matrix
Pop <- values(PopD.ALL)
r <- raster(PopD.ALL, 1)
r
class       : RasterLayer 
dimensions  : 288, 720, 207360  (nrow, ncol, ncell)
resolution  : 0.5, 0.5  (x, y)
extent      : -180, 180, -60, 84  (xmin, xmax, ymin, ymax)
coord. ref. : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
data source : in memory
names       : fourK 
values      : 5.611358e-07, 2.051069  (min, max)

GAM smoothing models

Justification for General Adative Models.

We need to justify our decision to use a GAM over other models. This should include citations to back up those arguments.

Fit and plot GAM model with different degrees of freedom

We should make our decisions very transparent here. We should be able to justify our decision of 3 degrees of freedom over other possible values.

Density projections

# Read the polygons
origins <- readShapePoly('Origins_updated.shp')
# Extract data
per.origin <- extract(r, origins, cellnumber = TRUE, buffer = 100000)
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
names(per.origin) <- origins@data[, 1]
str(per.origin)
List of 20
 $ W_African_Sav: num [1:309, 1:2] 92506 92507 92508 92509 92510 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Sudanic_Savan: num [1:306, 1:2] 99050 99051 99052 99053 99054 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ West Africa T: num [1:427, 1:2] 102609 102610 102611 103326 103327 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Ethipian plat: num [1:275, 1:2] 106281 106282 106283 106998 106999 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ NA           : num [1:195, 1:2] 67404 67405 67406 68119 68120 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ E_North_Ameri: num [1:170, 1:2] 64270 64271 64984 64985 64986 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ New_Guinea   : num [1:24, 1:2] 127360 127361 127362 128080 128081 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Mesoamerica  : num [1:73, 1:2] 93032 93033 93034 93035 93036 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ N_Lowland_SA : num [1:39, 1:2] 110373 110374 110375 111092 111093 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ NW_Lowland_SA: num [1:24, 1:2] 123319 123320 123321 123322 123323 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Sava_W_India : num [1:34, 1:2] 83312 84031 84032 84749 84750 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ S_India      : num [1:18, 1:2] 99153 99154 99872 99873 99874 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Ganges_E_Indi: num [1:92, 1:2] 85494 85495 85496 85497 85498 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Chinese_loess: num [1:84, 1:2] 72598 72599 73318 73319 73320 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Japanese     : num [1:36, 1:2] 59681 59682 60401 61121 61843 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Lower-MiddleY: num [1:131, 1:2] 72547 72548 72549 73267 73268 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ South trop ch: num [1:178, 1:2] 84818 84819 84820 84821 84822 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ NA           : num [1:258, 1:2] 62493 62494 62495 62496 62497 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ Southwes amaz: num [1:194, 1:2] 137758 137759 137760 137761 137762 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
 $ C/S_Andes    : num [1:165, 1:2] 137736 137737 137738 137739 137740 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : NULL
  .. ..$ : chr [1:2] "cell" "value"
par(mfrow=c(4,5), mar=c(0,0,0,0))
for(h in 1:20){
#h <- 3
originI <- Pop[per.origin[[h]][, 1], ]
x_values <- matrix(c(4:21), dim(originI)[1], 18, byrow=TRUE)
x_value_vector <- as.vector(x_values)
y_value_vector <- scale(as.vector(originI))
density_trend <- cbind(x_value_vector, y_value_vector)
plot(density_trend, col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(-10,10), xlim=c(21,4))
points(density_trend, cex=0.5, col=adjustcolor("cornflowerblue", 0.5))
}

par(mfrow=c(4,5), mar=c(0,0,0,0))
for(h in 1:20){
#h <- 3
originI <- Pop[per.origin[[h]][, 1], ]
x_values <- matrix(c(4:21), dim(originI)[1], 18, byrow=TRUE)
x_value_vector <- as.vector(x_values)
y_value_vector <- scale(as.vector(originI))
density_trend <- cbind(x_value_vector, y_value_vector)
plot(density_trend, col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(-4,8), xlim=c(21,4))
points(density_trend, cex=0.5, col=adjustcolor("grey", 0.1))
gammer <- loess(density_trend[,2] ~ density_trend[,1] )
summary(gammer)
lines(density_trend[,1] ,predict(gammer),  col="cornflowerblue", lwd=2)
}

span
the parameter α which controls the degree of smoothing.

The size of the neighbourhood is controlled by α (set by span or enp.target). For α < 1, the neighbourhood includes proportion α of the points, and these have tricubic weighting (proportional to (1 - (dist/maxdist)3)3). For α > 1, all points are used, with the ‘maximum distance’ assumed to be α^(1/p) times the actual maximum distance for p explanatory variables.

par(mfrow=c(4,5), mar=c(0,0,0,0))
for(h in 1:20){
#h <- 3
originI <- Pop[per.origin[[h]][, 1], ]
x_values <- matrix(c(4:21), dim(originI)[1], 18, byrow=TRUE)
x_value_vector <- as.vector(x_values)
y_value_vector <- scale(as.vector(originI))
density_trend <- cbind(x_value_vector, y_value_vector)
#points(density_trend, cex=0.5)
gammer <- loess(density_trend[,2] ~ density_trend[,1], span = .5)
summary(gammer)
predict_gam <- predict(gammer, se=TRUE)
plot(density_trend, col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(-1.35,1.35), xlim=c(21,4))
polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(-2, 2, 2, -2), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(-2, 2, 2, -2), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
abline(h=0, lty=2, col="grey")
lines(density_trend[,1] ,predict_gam$fit,  col="cornflowerblue")
lines(density_trend[,1] ,  predict_gam$fit + predict_gam$se.fit,  col="grey", lty=1)
lines(density_trend[,1] ,  predict_gam$fit - predict_gam$se.fit,  col="grey", lty=1)
}

# need to add a global mean, an everything but the origins mean, and a buffer around the origins mean. 
# Function standardization
std <- function(x) {
  b <- (x - min(x)) / (max(x) - min(x))
  return(rev(b))
}
diff_df <- function(h){ 
# Calculating mean and 
global.means <- global.SD <- list()
for (j in 1:length(per.origin)) {
  #print(j)
  originI <- Pop[per.origin[[j]][, 1], ]
  time <- 21:4
  originI <- na.exclude(originI)
  b <- apply(originI, 1, std)
  nJ <- nrow(originI)
  predictions <- matrix(nrow = nJ, ncol = length(time))
  colnames(predictions) <- as.character(time)
  for(i in 1:nJ) {
    
    # Need to show a gradient of these df values. 
    model <- gam(b[, i] ~ s(time, df = h))
    col <- sample(rainbow(100), 1)
    predictions[i, ] <- predict(model)
  }
  global.means[[j]] <- apply(predictions, 2, mean) 
  global.SD[[j]] <- apply(predictions, 2, sd)
}
names(global.means) <- paste(names(per.origin), "Means")
names(global.SD) <- paste(names(per.origin), "SD")
return(list(global.means, global.SD))
}
# Confirm that the x-axis is oriented correctly
for_3 <- diff_df(1)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
i <- 1
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,20))
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
originI <- Pop[per.origin[[1]][, 1], ]
#colnames(originI)
#plot(21:4, rep(0, length(21:4)), type="n", ylim=c(0,1), xlim=c(21,4), xaxt="n", yaxt="n")
for(j in 1:18){
points(23- c(jitter(rep(4, length(originI[,j])), 4.5)  + j), originI[,j], pch=19, cex=.1)
}
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]], type="b", pch=names(global.means[[i]]))
axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[1], 3, line=-2)

means_matrix <- matrix(rep(NA,19*20), 20, 19)
colnames(means_matrix) <- c("origin", rev(seq(4, 21, by=1)))
means_matrix[,1] <- names(global.means)
for(i in 1:20){
means_matrix[i,2:19] <- global.means[[i]]
}
kable(means_matrix, caption= "Mean values")
origin 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4
W_African_Sav Means 0.275750492966357 0.237971703906143 0.200504339081811 0.165047402018049 0.135516039740239 0.121748343406075 0.132429431895417 0.17103635569842 0.235948736377181 0.321617048802923 0.418964971526823 0.514676226549989 0.591121916502731 0.628378724452797 0.621163452983342 0.582047087468811 0.532681459452571 0.482909221409947
Sudanic_Savan Means -0.0186911478417769 -0.00828615401443568 0.00413446846041128 0.0215161762523414 0.0473073567212149 0.0847812201109172 0.136209309975754 0.20228390605606 0.282347797217804 0.374044632344897 0.472296827728429 0.568020597195695 0.648225465565203 0.697539021870325 0.713328901689326 0.707327373243822 0.697887725176853 0.69056153763021
West Africa T Means -0.0145401490853128 -0.00333603963380315 0.00977013345024412 0.027586956435481 0.0533165943413057 0.0895594750479319 0.138174778488521 0.199879802842878 0.274517388507917 0.360833593695506 0.45568720488448 0.552897898880818 0.643252356019774 0.715741781485123 0.768806992435192 0.809952043255802 0.850519193881187 0.893430170662931
Ethipian plat Means 0.0516408507031156 0.0622592531360626 0.0750787355293174 0.0933555709623621 0.12092332890413 0.16140265228906 0.217329358000213 0.28895304336974 0.373944304902601 0.467450912361356 0.562582640478741 0.650493007468181 0.722074582042064 0.768618080463592 0.790630347643354 0.797506826970228 0.803240018411344 0.812789660231236
NA Means 0.72808776413489 0.6723269776978 0.613165929035697 0.547108730705425 0.472515896153583 0.393590592158964 0.319669766181732 0.262708374009385 0.233548745835161 0.239616095881227 0.28323109870948 0.359870592475047 0.454992276384195 0.545528134731924 0.616545768777106 0.664148269449493 0.691583655592282 0.708950521834131
E_North_Ameri Means -0.0424144312128647 -0.0202618739720356 0.00475194649595462 0.0365915191653316 0.079541401163135 0.136467523436837 0.207873937132646 0.291025513809716 0.380397583621781 0.468564149521066 0.547361392244133 0.609663875755146 0.654835785797328 0.689283124023394 0.721880145858871 0.761679332218606 0.814909663949399 0.875153810181115
New_Guinea Means 0.304105470512681 0.28132745701113 0.25734789630324 0.230996250201583 0.201793192056862 0.171544911503563 0.144548456661618 0.127184052406642 0.126877035836262 0.15052865629083 0.203062414319868 0.285273581529037 0.389014353820968 0.496874952215665 0.597210277530265 0.683771044637899 0.754313180721177 0.816774228406938
Mesoamerica Means -0.0315889824677606 -0.00787599693194719 0.0184956204628149 0.0511692835844435 0.0938250236223921 0.148344738459587 0.214601573425648 0.290380258066549 0.372334867390379 0.456479966860125 0.538354702268212 0.613001244481024 0.676612820283987 0.726625668176205 0.767020170677251 0.80679724213028 0.855043623685109 0.908351302981932
N_Lowland_SA Means 0.208792535197897 0.197230324856633 0.185079121786267 0.171696272010441 0.156804931838545 0.141342946965234 0.128176787393512 0.122340507893562 0.130435008736839 0.159548596595071 0.215485053059509 0.300036154887671 0.405861213383308 0.51607541749585 0.62000422933541 0.712583747106496 0.792272847070064 0.866211062729842
NW_Lowland_SA Means 0.326576386801442 0.312436135756889 0.296990439986673 0.278723633997093 0.256416348833303 0.230169366346516 0.201945873000531 0.175714919736147 0.157651360929879 0.155352073191265 0.176275702224548 0.225642677767534 0.302153168560349 0.396329228756827 0.497310353388214 0.594432476311419 0.67925446713634 0.756553171147025
Sava_W_India Means -0.0237936944828927 -0.00818464775151594 0.00933560457136895 0.0313826871867378 0.0607897006722834 0.0992817835941126 0.147568966381951 0.205468601119744 0.272443196878899 0.347413657258897 0.428584371379107 0.513039004997093 0.595722652725526 0.669265301648986 0.731180489316986 0.788223314024364 0.850666362502511 0.917274849593167
S_India Means -0.0222028081854339 -0.0066002592031116 0.0109240264309662 0.0332350046742644 0.0636053304857559 0.104248025366543 0.156161312176903 0.218860716380081 0.291071667647164 0.371586637639489 0.458699358753368 0.549398894270441 0.638133144838091 0.71736832702396 0.786036841922908 0.849257343160103 0.913846434565112 0.979674443478567
Ganges_E_Indi Means -0.0168749067644347 -0.00665207444708958 0.00516238304586039 0.0208799296723999 0.0431774421109922 0.0742138287818073 0.115649991879242 0.168563999805984 0.233555951882637 0.310487513335769 0.398078302603856 0.492768744130255 0.588625507090279 0.676929905267031 0.753772199676962 0.823106046514196 0.892776064568763 0.964026386513837
Chinese_loess Means -0.00992922030088753 -0.00685627234272808 -0.00263644972242058 0.00456650135793812 0.0171800768542588 0.0379487356429578 0.0695048935574124 0.114680636092733 0.176234630227922 0.255681643811977 0.353044690591995 0.465903186889885 0.587480671879438 0.70545496017147 0.811956397518547 0.90571144015868 0.990020919073498 1.06943656618837
Japanese Means 0.474649163724578 0.443432703865345 0.410041741204845 0.372273786700216 0.329121724356353 0.283030955690219 0.240090867441392 0.209371090119366 0.201589325186606 0.226840139404003 0.291350184139259 0.39377817553382 0.519726499901562 0.642890482156585 0.747382040461932 0.829407324688329 0.892195580878682 0.945280306169006
Lower-MiddleY Means -0.00682865849885968 -0.00060483620796883 0.00671174779516591 0.0168353119264841 0.0318371795131959 0.0536523053498361 0.0841840911894777 0.125268923860985 0.179000307645022 0.247353016268821 0.331229454779227 0.42919493710873 0.535517759646172 0.639543869787761 0.736041145928061 0.82613958614389 0.915048715480776 1.00384399368775
South trop ch Means -0.00259675023606447 -0.00369446566682659 -0.00363747351558766 -0.000390054740314468 0.00904019752001561 0.0284916546492706 0.0620623767539311 0.113139640613902 0.183967610626003 0.275388397726442 0.385135385537217 0.507968233105058 0.634326208132707 0.750251125909705 0.848539337462573 0.930537024584384 1.00231564635787 1.06963296926003
NA Means 0.0366402042172722 0.0345449445801444 0.0333093635431334 0.0345629129341452 0.0409323268055525 0.0561025771005159 0.0840836906480487 0.12805515000113 0.189442050381472 0.269535827938253 0.368930130834347 0.484509427569726 0.606456684388843 0.720252238756432 0.817753922638379 0.899780585526795 0.971748613294788 1.03906371492767
Southwes amaz Means 0.207835723880993 0.197019933600991 0.185689737006914 0.173364610555289 0.159843367441753 0.145872982114604 0.134154420414965 0.129609533908725 0.138844389475622 0.168981654647338 0.225948263430072 0.312180448593161 0.422378015176177 0.542599962121189 0.664662002239541 0.784132607465062 0.897503322879635 1.00679099727573
C/S_Andes Means 0.0291205853249027 0.0314816768181023 0.0344713731256695 0.0390464429788137 0.0464560633526933 0.0581169360685076 0.0760540915093959 0.103031413769306 0.142906851931112 0.200040121010661 0.27794292932455 0.377058478195417 0.491456226460239 0.608384004959301 0.721451798462705 0.828972489197 0.930712639008333 1.02909296975965
#global.SD
SD_matrix <- matrix(rep(NA,19*20), 20, 19)
colnames(SD_matrix) <- c("origin", rev(seq(4, 21, by=1)))
SD_matrix[,1] <- names(global.SD)
for(i in 1:20){
SD_matrix[i,2:19] <- global.SD[[i]]
}
kable(SD_matrix, caption= "SD values")
origin 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4
W_African_Sav SD 0.186556185173684 0.159071135711959 0.130974576751884 0.101946183025733 0.0724951714757066 0.0464817364491077 0.0281882850407625 0.0212718909296576 0.0230484233864053 0.0260000666669227 0.0272778672869396 0.0272414655989988 0.0286145237100166 0.0359445310006679 0.0509667284519141 0.0718957662099432 0.0961865477719618 0.12156398251189
Sudanic_Savan SD 0.0182791317887036 0.0120186235797875 0.00857406807198337 0.0119997090375925 0.0200097740504662 0.0296208384871706 0.0390634218166876 0.0465027632519908 0.0502676895837266 0.0490728899403298 0.0422563308391379 0.0301155921728213 0.016251502147543 0.0230519738470708 0.0490762671854076 0.0798060762063573 0.111190090221826 0.142489654117473
West Africa T SD 0.0128551006323539 0.0100809743903953 0.0110855392306364 0.0157356177847031 0.0225339267643659 0.0302798766216314 0.0378753478987503 0.0441002370122807 0.0478360621585905 0.0482472418609378 0.045098717097735 0.0390673319501593 0.0318512113726889 0.0254461299782974 0.0263553160311764 0.0393349506349416 0.0572833097318681 0.0763495674818114
Ethipian plat SD 0.198659638310769 0.170440069868076 0.141737372134567 0.112259279537512 0.0864755397538964 0.0791421681652602 0.0986717402217165 0.129156174657549 0.154623472712395 0.166247254796878 0.159947337518384 0.135808529359533 0.0994473010536208 0.0618393023227622 0.0356919120363483 0.0377802530877869 0.0546872860266305 0.0726120006791913
NA SD 0.352588159054744 0.332443095173091 0.310979361000686 0.28580375866142 0.254547237522766 0.216346143796596 0.171980702025272 0.12388521679558 0.0763676236214709 0.0403854093134876 0.0435516738756018 0.0673123480707615 0.0842474074682211 0.089847619869054 0.0865158533690929 0.0824620916709309 0.0858640772961775 0.09604764429718
E_North_Ameri SD 0.00744774460623942 0.00688305183133896 0.00730077417171542 0.00859083907761313 0.0105320687647222 0.012800810910875 0.0151914913730156 0.0175920880323135 0.0199689872021909 0.0222421032252577 0.0241465903979098 0.0252306084926904 0.0249032846153157 0.0225138982726739 0.0181697023167219 0.0136609854949669 0.0121135163669742 0.014408338225588
New_Guinea SD 0.0890975299550152 0.0842301251797607 0.0792178489696074 0.0736641677047341 0.0671594485979282 0.0596008898697251 0.0511674521224338 0.0422240170397645 0.0331812675142621 0.0254299321136062 0.0225457007202054 0.0268237812941903 0.034037094432116 0.0390786810653157 0.0406181672896982 0.0401664674846312 0.0399927675349423 0.0409680658412061
Mesoamerica SD 0.0257631275045289 0.0187178864900728 0.0164812107253495 0.0223842305919749 0.0343001607587918 0.0492203013799705 0.0648668376274174 0.0787357939871162 0.0882653199553832 0.0913017452354271 0.0865857410678889 0.0743419528904328 0.0572427399139474 0.0406792417457969 0.030609493113632 0.0315030760258884 0.0386540722319049 0.0479903934364773
N_Lowland_SA SD 0.111921322285171 0.107282514497114 0.102185138216149 0.0958207981245285 0.0873593968043197 0.0763936956444485 0.0630414035072374 0.0480814037523411 0.0329504357663719 0.0219371014627934 0.0252549283205093 0.0397679138235974 0.0556648469342838 0.0682249344844884 0.0766047903929501 0.0827208213023969 0.0895838817981019 0.0974704711325054
NW_Lowland_SA SD 0.150541353866891 0.139669442413694 0.127930041006379 0.114205838438166 0.097868424572761 0.0797876044778232 0.0631128649695468 0.0525350681168884 0.0499851737421644 0.0520614502101073 0.0541664339731254 0.054016322802996 0.0513832224992821 0.0467970105936129 0.0411427020149635 0.0364198792817815 0.035220746530383 0.0381254553823437
Sava_W_India SD 0.00620248739705606 0.00409602037065882 0.00439841375218349 0.00750428764031471 0.012286775530684 0.0183044382262446 0.0252698645356455 0.0327879406646454 0.0403222428411792 0.0470625286607487 0.0518738127485427 0.0537645121764797 0.052235535975566 0.0476849083553341 0.0415125953320544 0.0349790611537332 0.029039548251698 0.0251114044895353
S_India SD 0.0085115048531172 0.00892906518867892 0.00967136329810452 0.0109786376784981 0.0132686066270033 0.0165765384328679 0.0204467930723038 0.0238711849145664 0.0256672972233344 0.0255092175722659 0.0237276529091089 0.0208724202116767 0.0181457061716282 0.0170301004732513 0.0168873351736634 0.0164690070990293 0.0154340912923534 0.0142507144708916
Ganges_E_Indi SD 0.00996215193394363 0.00691767159299303 0.00791433587724963 0.0127874855691734 0.0199162980428461 0.0287137566212716 0.0388527650554929 0.0499222314748722 0.0614506116687209 0.0728233254374634 0.0831495621605526 0.0908947825786612 0.0944845150273855 0.0928545508935936 0.0864932764809146 0.0768625361267711 0.065847656098237 0.0558662960341165
Chinese_loess SD 0.00723695180791585 0.00653465042035558 0.0067229060136461 0.00783510017868662 0.00968749896229179 0.0121031590893252 0.015015434915449 0.0186404465048965 0.0229918308268338 0.0276609710250012 0.0323906245272664 0.0365700364119769 0.0388300984431191 0.037141136645161 0.0311556397194864 0.0229315384793928 0.0156852378394716 0.0147092261255239
Japanese SD 0.184696194095272 0.167622323188328 0.150274927059077 0.131797262192788 0.11137082376895 0.0892794740360921 0.0676920587877228 0.050106916646986 0.0386317289017512 0.0331345985067326 0.0322763726395578 0.0340554941652883 0.0358963772505133 0.0361379405079019 0.035343175991101 0.0349568839559365 0.036562520951131 0.0402092257222996
Lower-MiddleY SD 0.0109221052239635 0.00879404210265073 0.0082644102269953 0.00985094611053262 0.0133492834979398 0.0182250521629163 0.0238393891749069 0.0293168212659387 0.0336239347179238 0.0358993675826794 0.0357122875762433 0.033336309677034 0.0300883638849522 0.0274478338873639 0.0261092333651014 0.0261920192405151 0.0270668753710159 0.0286050078015116
South trop ch SD 0.0164074485323459 0.013017339693911 0.0101269327626496 0.00883966436288355 0.0113546594405518 0.0176935756740366 0.0263781784905157 0.0362001386983728 0.0458282304601001 0.0540734242720755 0.0596617127431108 0.0616233193553812 0.0592826758862225 0.0525468261222113 0.0423612740395727 0.0308335216922742 0.0220855802940787 0.0229498120978104
NA SD 0.0809467917305336 0.0685832123328493 0.0557119272621779 0.0416794929850676 0.0273556018582627 0.0213125874557977 0.0336477364276112 0.0522922853903463 0.0688255532152485 0.0796532138108896 0.0829295203707789 0.0782121775868238 0.0673634830545416 0.0546060927712949 0.0437646882775398 0.0377464374007277 0.0370323136420871 0.0390839743471241
Southwes amaz SD 0.125774207173705 0.115361452592516 0.1042880086271 0.0916253149336918 0.0769919993552501 0.0614840306437265 0.0481765788042826 0.0417025596083742 0.0432490383179266 0.0477994697641187 0.0500604213341766 0.0477221942386258 0.0415134022061204 0.0341998323542236 0.0287859842127018 0.0282643985012614 0.0333826815416954 0.0417094659365358
C/S_Andes SD 0.0727773302277296 0.06676048268613 0.0609678447564098 0.055024169996668 0.0491091885343267 0.0446462966444592 0.0438008333720804 0.0470055485124615 0.0524694588100196 0.0582765439649155 0.0633094382982524 0.0669266582058461 0.068773937206034 0.0681584149345244 0.0650020480377401 0.0612611199316851 0.059915336729057 0.0611532400816508
par(mfrow=c(4,5), mar=c(0,0,0,0))
for(j in 1:20){
plot(means_matrix[1,2:19], col=adjustcolor("cornflowerblue", alpha=0.8), pch=names(means_matrix[1,2:19]), type="n", xlab="year", ylab="Density", xaxt="n", ylim=c(0,1))
originI <- Pop[per.origin[[j]][, 1], ]
for(h in 1:18){
points(23- c(jitter(rep(4, length(originI[,h])), 4.5)  + h), originI[,h], pch=19, cex=.1)
}
  
lines(means_matrix[j,2:19], col=adjustcolor("cornflowerblue", alpha=0.8), pch=names(means_matrix[j,2:19]), type="b", xlab="year", ylab="Density", xaxt="n")
}
axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(1)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
  
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))  
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using one degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(2)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using two degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(3)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using three degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(4)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using four degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(5)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using 5 degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(10)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))  
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using 10 degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(12)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))  
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using 12 degree of freedom

par(mfrow=c(4,5), mar=c(0,0,0,0))
for_3 <- diff_df(17)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]
for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")
polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))
polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))   
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])
#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}

GAM model using 17 degree of freedom

Productivity

# Load patricks productivity PCA data
load('Productivity_ALL.RDATA')
# Load origin shapefiles
origins <- readShapePoly('Origins_updated.shp')
origin.time.region <- c(2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 
                        2, 2, 1, 2, 2, 2, 2, 2, 2, 2) # 1 = early; 2 = middle
# Extract the data
prod.origin <- extract(Productivity.ALL, origins)
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
# Mean and SD per region
means <- lapply(prod.origin, colMeans, na.rm = TRUE)
sds <- lapply(prod.origin, sd, na.rm = TRUE)
names(means) <- origins@data$CONTINENT
ymax <- max(unlist(means))
ymin <- min(unlist(means))
time <- 4:21
# Plot
#pdf("productivity.pdf", 20, 30) 
par(mfrow = c(5, 4), mar = c(2, 2, 2, 0))
for (i in 1:length(means)) {
  plot(y = means[[i]], x = time, xlim = c(21, 4), ylim = c(ymin, ymax),
       main = names(means)[i], cex.main = 1, cex.lab = 1, cex.axis = 1,
       ylab = "Productivity (PCA axis)", xlab = "Thousand of years ago (k)",
       pch = 20, lwd = 1, type = "l", 
       col = c("purple", "green")[origin.time.region[i]])
  up <- sds[[i]] + means[[i]]
  down <-  means[[i]] - sds[[i]]
  lines(up ~ time, lty = 2)
  lines(down ~ time, lty = 2)
  
}

#dev.off()

Compare rates between origins and not-origins

Compare rates between different time periods

Setup final figure

Frame in the layout

a <- layout(matrix(c(
    1, 1, 1, 1, 1, 1, 1, 1,
    3,  6, 7, 8, 9, 10, 11, 4, 
    3,  5, 5, 5, 5, 5, 5,   4, 
    3,  12, 13, 14, 15, 16, 17, 4,
    2, 2, 2, 2, 2, 2, 2, 2
    ), 5, 8, byrow=TRUE), width=c(1, 1, 1, 1, 1, 1, 1, 1), height=c(0.5, 1, 1.5, 1, 0.5))
layout.show(a)

Make blank template plots

frameplot <- function(){
    plot(21:0,rep(0, 22), xlim=c(17,4), ylim=c(0, 2.25), type="n", xaxt="n", yaxt="n", xlab="", ylab="")
}
frameplot_bottom <- function(){
    plot(21:0,rep(0, 22), xlim=c(17,4), ylim=c(-0.25, 2), type="n", xaxt="n", yaxt="n", xlab="", ylab="")
}
frameplot()

frameplot_bottom()

map for final figure

Make the map for the center panel (#5 on layout panel)

d <- readPNG("earth.png")
png(file=paste("40962.png",sep=""),width=2000,height=1000, bg="transparent")
par(mar=c(0,0,0,0))
plot(seq(-180, 180, length.out = 19), seq(-90, 90, length.out = 19), type="n",xlim=c(-180, 180),ylim=c(-90, 90), xaxt="n")
rasterImage(d, -180, -90, 180, 90, interpolate=TRUE, col=d)
polygon(x=c(-180,-180, 180,180), y=c(-90, 90, 90, -90), col=adjustcolor("white", alpha=0.1))
#rasterImage(d, -13.5, -13.5, 375, 375, interpolate=TRUE, col=d)
plot(origins_subset, add=TRUE, col=adjustcolor("white", alpha=.8), xaxt="n", border="white", lwd=4) #still need to reproject!!!
dev.off()
null device 
          1 

Trend through time panel

Setup the plot template for small panel plots (#6-17 on layout panel)

###################
type_number <- 8
complex_figure <- function(type_number, i, means, sds){
                        
if(i < 6)   polygon(x=c(12,12,8.2,8.2), y=c(-1,3,3,-1), col=adjustcolor("cornflowerblue", alpha=0.4), border=NA)                    
if(i > 5)   polygon(x=c(8.2,8.2,4.2,4.2), y=c(-1,3,3,-1), col=adjustcolor("limegreen", alpha=0.4), border=NA)
                                    
    match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
    maxer <- max(match, na.rm=TRUE)
    j <- ecdf(maxer-match)
    print(j)
    
x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- -c(0, j(seq(0, maxer, length.out=100)))
#lines(x_seq, y_seq, type="l", ylim=c(-1,1))
#polygon(c(0, x_seq), c(0, y_seq), border="black", col=adjustcolor("cornflowerblue", alpha=0.5))
#abline(v= maxer - quantile(j)[2])
    
    break_one_1 <- maxer
            break_two_1 <- maxer - quantile(j)[2]
                
#   polygon(x=c(break_two_1, break_two_1, break_one_1, break_one_1), y=c(0, 1, 1, 0), col=adjustcolor("cornflowerblue", alpha=0.5), border=NA)
            
    match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 10]
    maxer <- max(match, na.rm=TRUE)
    j <- ecdf(maxer-match)
    print(j)
    
x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- 2+c(0, j(seq(0, maxer, length.out=100)))
#lines(x_seq, y_seq)
#polygon(c(0, x_seq), c(2, y_seq), border="black", col=adjustcolor("limegreen", alpha=0.5))
    
    break_one_2 <- maxer
            break_two_2 <- maxer - quantile(j)[2]
                
#   polygon(x=c(break_two_2, break_two_2, break_one_2, break_one_2), y=c(1, 2, 2, 1), col=adjustcolor("limegreen", alpha=0.5), border=NA)
            
    
        #abline(v=11)
    type <- 1
        
        if(type == 1){
    x <- c(means[[i]] , means[[i]]  + abs(sds[[i]]), means[[i]]  - abs(sds[[i]]))
    scaled <- scale(x , center=FALSE)
    meanss <- scaled[1:18]
    sdss_plus <- scaled[19:36]
    sdss_minus <- scaled[37:54]
    #abline(v=10, col="red")
    length(scaled)
    #lines(4:21, means[[i]] + sds[[i]])
    #polygon(x=c(4:21, 21:4), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")
    polygon(x=c(21:4,4:21), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white") 
    }
    
    if(type == 2){
    x <- c(means[[i]] , means[[i]]  + abs(sds[[i]]), means[[i]]  - abs(sds[[i]]))
    scaled <- x + 1 #scale(x , center=FALSE)
    meanss <- scaled[1:18]
    sdss_plus <- scaled[19:36]
    sdss_minus <- scaled[37:54]
    #abline(v=10, col="red")
    length(scaled)
    #lines(4:21, means[[i]] + sds[[i]])
    polygon(x=c(4:21, 21:4), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")    
    }
if(type == 3){
    x <- c(means[[i]] , means[[i]]  + abs(sds[[i]]), means[[i]]  - abs(sds[[i]]))
    scaled <- x #scale(x , center=FALSE)
    meanss <- scaled[1:18]
    sdss_plus <- scaled[19:36]
    sdss_minus <- scaled[37:54]
    #abline(v=10, col="red")
    length(scaled)
    #lines(4:21, means[[i]] + sds[[i]])
    polygon(x=c(4:21, 21:4), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")    
    }
    
    
means_long_y <- c(1,1,1,1,1, meanss)
means_long_x <- c(0:4, 4:21)
 
            break_one <- break_one_2
            break_two <- break_two_2
        #       polygon(x=c(break_one, break_one, 22, 22), y=c(1, 2, 2, 1), col=adjustcolor("white", alpha=0.8), border=NA)
        #       polygon(x=c(break_two, break_two, break_one, break_one), y=c(1, 2, 2, 1), col=adjustcolor("white", alpha=0), border=NA)
            #   polygon(x=c(-1,-1, break_two , break_two), y=c(1.9, 3.1, 3.1, 1.9), col=adjustcolor("white", alpha=0.8), border=NA) 
                #abline(v= break_one, col="white")
                #abline(v= break_two, col="white")
                
                break_one <- break_one_1
            break_two <- break_two_1
        #       polygon(x=c(break_one, break_one, 22, 22), y=c(0, 1, 1, 0), col=adjustcolor("white", alpha=0.8), border=NA)
        #       polygon(x=c(break_two, break_two, break_one, break_one), y=c(0, 1, 1, 0), col=adjustcolor("white", alpha=0), border=NA)
            #   polygon(x=c(-1,-1, break_two , break_two), y=c(-1.1, .1, .1, -1.1), col=adjustcolor("white", alpha=0.8), border=NA) 
                #abline(v= break_one, col="white")
                #abline(v= break_two, col="white")
                
#lines(x=c(break_one_2, break_one_2), y=c(1,3), col="white")
#lines(x=c(break_one_1, break_one_1), y=c(1,-1), col="white")
#lines(x=c(break_two_2, break_two_2), y=c(1,3), col="white")
#lines(x=c(break_two_1, break_two_1), y=c(1,-1), col="white") 
#lines(4:21, meanss)
    lines(21:4, meanss)
    
}
frameplot()
complex_figure(7, 1, global.means, global.SD) 
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:7] =      0,    0.5,      1,  ...,      5,    5.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:4] =      0,    3.5,      4,    4.5
axis(1)
axis(2)

Assemble the figure

Assemble the figure

quartz(width=8, height=8)
layout(matrix(c(
    1, 1, 1, 1, 1, 1, 1, 1,
    3,  6, 7, 8, 9, 10, 11, 4, 
    3,  5, 5, 5, 5, 5, 5,   4, 
    3,  12, 13, 14, 15, 16, 17, 4,
    2, 2, 2, 2, 2, 2, 2, 2
    ), 5, 8, byrow=TRUE), width=c(1, 1, 1, 1, 1, 1, 1, 1), height=c(0.5, 1, 1.5, 1, 0.5))
par(mar=c(0,0,0,0))
# 1-4 label margins
blankplot <- function(){
    
    plot(0,0, xlim=c(4,21), ylim=c(1, 1.25), bty="n", type="n", xaxt="n", yaxt="n", xlab="", ylab="")
}
blankplot()
blankplot()
blankplot()
blankplot()
origins <- readShapePoly('Origins_updated.shp')
origin.time.region <- c(2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 
                        2, 2, 1, 2, 2, 2, 2, 2, 2, 2) # 1 = early; 2 = middle
as.character(origins$CONTINENT)
 [1] "W_African_Sav" "Sudanic_Savan" "West Africa T" "Ethipian plat" NA             
 [6] "E_North_Ameri" "New_Guinea"    "Mesoamerica"   "N_Lowland_SA"  "NW_Lowland_SA"
[11] "Sava_W_India"  "S_India"       "Ganges_E_Indi" "Chinese_loess" "Japanese"     
[16] "Lower-MiddleY" "South trop ch" NA              "Southwes amaz" "C/S_Andes"    
#subset_order <- c(1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 17, 18)
subset_order <- c(8, 10, 9, 5, 18, 7, 6, 20, 1, 2, 13, 16)
origins_subset <- origins[subset_order,]
origins_subset$CONTINENT
 [1] Mesoamerica   NW_Lowland_SA N_Lowland_SA  <NA>          <NA>          New_Guinea   
 [7] E_North_Ameri C/S_Andes     W_African_Sav Sudanic_Savan Ganges_E_Indi Lower-MiddleY
18 Levels: C/S_Andes Chinese_loess E_North_Ameri Ethipian plat Ganges_E_Indi ... West Africa T
d <- readPNG("earth.png")
png(file=paste("40962.png",sep=""),width=2000,height=1000, bg="transparent")
par(mar=c(0,0,0,0))
plot(seq(-180, 180, length.out = 19), seq(-90, 90, length.out = 19), type="n",xlim=c(-180, 180),ylim=c(-90, 90), xaxt="n")
rasterImage(d, -180, -90, 180, 90, interpolate=TRUE, col=d)
polygon(x=c(-180,-180, 180,180), y=c(-90, 90, 90, -90), col=adjustcolor("white", alpha=0.1))
#rasterImage(d, -13.5, -13.5, 375, 375, interpolate=TRUE, col=d)
plot(origins_subset, add=TRUE, col=adjustcolor("white", alpha=.8), xaxt="n", border="white", lwd=4) #still need to reproject!!!
dev.off()
quartz 
     2 
d <- readPNG("40962.png")
dim(d)
[1] 1000 2000    4
par(mar=c(0,0,0,0))
plot(0:360,0:360,type="n",xlim=c(20,360),ylim=c(65,295), yaxt="n", xaxt="n")
rasterImage(d, -28.5, -13.5, 388, 375, interpolate=TRUE, col=d)
axis(2, label=seq(-90, 90, length.out = 19), at=seq(1, 360, length.out = 19), las=1)
mtext("latitude", 2, line=4, at=180)
abline(h=seq(1, 360, length.out = 19), col=adjustcolor("grey10", alpha= 0.4), lwd=1)
abline(h=180, col=adjustcolor("white", alpha= .5), lwd=1)
load('PopD_all_December.rdata')
# Extract the data
prod.origin <- extract(PopD.ALL, origins_subset)
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
NOTE: rgdal::checkCRSArgs: no proj_defs.dat in PROJ.4 shared files
library(matrixStats)
matrixStats v0.51.0 (2016-10-08) successfully loaded. See ?matrixStats for help.
# Mean and SD per region
means <- lapply(prod.origin, colMeans, na.rm = TRUE)
sds <- lapply(prod.origin, colSds, na.rm = TRUE)
## new values from Bruno's GAM model (produced in script called Population_Trend_per_y.R)
means <- global.means
sds <- global.gams
names(means) <- origins_subset@data$CONTINENT
ymax <- max(unlist(means))
ymin <- min(unlist(means))
time <- 4:21
#plot(origins)
#means[[1]] +
#sds[[1]]
#scale(as.numeric(means[[1]]), center=FALSE)
name_vector <- as.character(origins_subset@data$CONTINENT)
for(i in 1:12){
    
    if(i > 6){frameplot()}else{frameplot_bottom()}
    
        ## customize polygons for each graph
    if(i == 1){ #mesoamerica  #values from Larson
        
            complex_figure(3, i, means, sds)
                
    
        }
    
    
    #########
    if(i == 2 ){ #NW lowlands SA  #values from Larson
        
        complex_figure(6, i, means, sds)
    
        }
        
        #########
    if( i == 3){ #NW lowlands SA  #values from Larson
        
        complex_figure(6, i, means, sds)
        
        }
        #########
    if(i == 4){ #Fertile crescent aka Southwest asia  #values from Larson
        
        
    complex_figure(8, i, means, sds)
                
        }
        
        #########
    if(i == 5){ #loess plateau  #values from Larson
        
        complex_figure(2, i, means, sds)
            
        }
        
        
        #########
    if(i == 6){ #new guinea  #values from Larson
        
        complex_figure(4, i, means, sds)
        
        }
#########
    if(i == 7){ #Eastern N.A.  #values from Larson
        
        complex_figure(5, i, means, sds)
        
            }
        #########
    if(i == 8){ #Andes  #values from Larson
        
        complex_figure(6, i, means, sds)
        
                }
#########
    if(i == 9){ #W. African Sav  #values from Larson
        
        complex_figure(1, i, means, sds)
        
            }
#########
    if(i == 10){ #Sudanic sav  #values from Larson
        
        complex_figure(1, i, means, sds)
        
                }
#########
    if(i == 11){ #Ganges  #values from Larson
        
        
        complex_figure(7, i, means, sds) 
        
        }
#########
    if(i == 12){ #loess  #values from Larson
        
        complex_figure(2, i, means, sds)
         
                }
        
        
        #lines(4:21, means[[i]])
        
        abline(h = 1, col=adjustcolor("forestgreen", alpha=.5), lty=2)
        
    # add axes to some locations
    if(i == 1 | i == 7){axis(2, at=seq(0,2, by=0.25), label=seq(0,2, by=0.25), las=1)}
    if(i == 6 | i == 12){axis(4, at=seq(0,2, by=0.25), label=seq(0,2, by=0.25), las=1)}
    #if(i == 6 | i == 12){axis(4, at=seq(2,3, by=0.25), label=seq(0,1, by=0.25), las=1)
    #   axis(4, at=seq(-1,0, by=0.25), label=rev(seq(0,1, by=0.25)), las=1)
    #   }
    if(i > 6){axis(1)} else{axis(3)}
    
    # add text 
    if(i < 7){polygon(x=c(-30, -30, 30, 30), y=c(-0.1, -0.5, -0.5, -0.1), col="black")
    mtext(name_vector[i], 1, line=-1.2, col="white", cex=0.5)}
    
    if(i > 6){polygon(x=c(-30, -30, 30, 30), y=c(2.1, 2.5, 2.5, 2.1), col="black")
    mtext(name_vector[i], 3, line=-1.2, col="white", cex=0.5)}
    
    # add axis labels
    if(i == 1 | i ==  7){mtext("scaled density potential", 2, line=4, at=1)}
    if(i ==  3){mtext("Thousand years before present", 3, line=3.5, at =5)}
    if(i ==  9){mtext("Thousand years before present", 1, line=3.5, at =5)
        
        }
    
}
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:4] =      0,      4,      7,      8
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:5] =      0,      1,      4,      7,      8
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:8] =      0,      1,      2,  ...,      5,      6
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:9] =      0,      1,      2,  ...,      6,    6.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:8] =      0,      1,      2,  ...,      5,      6
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:9] =      0,      1,      2,  ...,      6,    6.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:6] =      0,    0.5,      1,  ...,      2,      8
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:8] =      0,    0.5,   0.75,  ...,      5,      7
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,    0.5,      2,  ...,   7.75,    9.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:9] =      0,    0.5,      1,  ...,    4.5,    7.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:1] =      0
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:2] =      0,      4
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:3] =      0,    0.5,   1.75
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:3] =      0,      1,   1.25
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:8] =      0,      1,      2,  ...,      5,      6
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:9] =      0,      1,      2,  ...,      6,    6.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,   0.25,   1.25,  ...,   6.75,   7.75
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,   2.25,   2.75,  ...,   5.75,   6.25
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,   0.25,   1.25,  ...,   6.75,   7.75
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,   2.25,   2.75,  ...,   5.75,   6.25
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:7] =      0,    0.5,      1,  ...,      5,    5.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:4] =      0,    3.5,      4,    4.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:11] =      0,    0.5,      2,  ...,   7.75,    9.5
Empirical CDF 
Call: ecdf(maxer - match)
 x[1:9] =      0,    0.5,      1,  ...,    4.5,    7.5
saveToPDF <- function(...) {
    d = dev.copy(pdf,...)
    dev.off(d)
}
saveToPNG <- function(...) {
    d = dev.copy(png,...)
    dev.off(d)
}
## Try them out
saveToPDF("my.pdf", height=8,width=8)
quartz 
     2 
saveToPNG("my.png", height=8, width=8, units="in", res=300)
quartz 
     2 
dev.off()
null device 
          1 
---
title: "Origins of agriculture density analysis"
author: "Ty Tuff"
date: 'project began: September 2016, document updated: `r strftime(Sys.time(), format
  = "%d %B %Y")`'
output:
  html_notebook: default
  word_document: default
---
## Current best version
![Figure 1 - This figures shows...](my.png)





## Code
1. [R environment setup](#r-environment-setup)
2. [Setting time breaks](#setting-time-breaks)
3. [Defining origins](#defining-origins)
4. [Import raster data](#import-raster-data)
5. [GAM smoothing models](#gam-smoothing-models)
6. [Compare rates between origins and not-origins](#compare-rates-between-origins-and-not-origins)
7. [Compare rates between different time periods](#compare-rates-between-different-time-periods)
8. [Setup final figure](#setup-final-figure)
9. [Map for final figure](#map-for-final-figure)
10. [Trend through time panel for final figure](#trend-through-time-panel)
11. [Assemble and print final figure](#assemble-the-figure)



## R environment setup
#### Attach libraries
```{r}
library(png)
library(maptools)
library(raster)
library(gam)
```



#### Set working directory
```{r}
setwd("~/Desktop/Botero postdoc 2016/Human density and the origins of agriculture/")
```



## Setting time breaks
#### Define the times of agricultural origins
![](Larson_dates.jpg)

```{r}
par(mar=c(0,0,0,20))
d <- readPNG("Larson_dates.png")
plot(seq(0,18, length.out = 19), seq(0,36, length.out = 19), type="n",ylim=c(0,36),xlim=c(0, 18), xaxt="n")

rasterImage(d, 0,0,18,36, interpolate=TRUE, col=d)



Start_of_early_window <- 16-12
End_of_early_window_start_of_late_window <- 8.2
End_of_late_window <- 17-4.2

polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(0, 34, 34, 0), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(0, 34, 34, 0), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

```



These dates are provided in the supplimentary information for the Larson (2014) paper. I've copied those values into a .csv table provided here. 

```{r}
domestication_times <- read.csv("Domestication timing larson 2014.csv")

dim(domestication_times)
```

```{r, echo=FALSE}
library(knitr) 
kable(domestication_times, caption= "This is our world")
```


```{r}
par(mar=c(5,4,6,1))

dates <- unlist(domestication_times[3:8])
hist(dates, breaks = 22, xlim=c(15,0), xlab="K years ago", col=adjustcolor("cornflowerblue", alpha= 0.5), border=adjustcolor("cornflowerblue", alpha= 0.9), main="All dates in dataset"  )
mtext("This tells us about how evenly our evidence is distributed in time", 3, line=1)


```

```{r}
hist(dates, breaks = 22, xlim=c(15,0), xlab="Thousand years ago", col=adjustcolor("cornflowerblue", alpha= 0.5), border=adjustcolor("cornflowerblue", alpha= 0.9), main="All dates in dataset with Larson(2014) date windows")

Start_of_early_window <- 12
End_of_early_window_start_of_late_window <- 8.2
End_of_late_window <- 4.2

polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

hist(dates, breaks = 22, xlim=c(15,0), xlab="K years ago", col=adjustcolor("cornflowerblue", alpha= 0.2), border=adjustcolor("cornflowerblue", alpha= 0.9), main="", add=TRUE)

mtext("Early Holocene", 3, line = -1, adj=.3)
mtext("Middle Holocene", 3, line= -1, adj=.6)

```

```{r}

par(mfrow=c(2,3), mar=c(4,4,2,0))
dim(domestication_times)
specific_dates <- domestication_times[,3:8]

for(i in c(1, 3, 5, 2, 4, 6)){
hist(specific_dates[,i], breaks = 22, xlim=c(15,0), xlab="Thousand years ago", col=adjustcolor("cornflowerblue", alpha= 0.5), border=adjustcolor("cornflowerblue", alpha= 0.9), main= names(specific_dates)[i])

Start_of_early_window <- 12
End_of_early_window_start_of_late_window <- 8.2
End_of_late_window <- 4.2

polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(0, 30, 30, 0), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

hist(specific_dates[,i], breaks = 22, xlim=c(15,0), xlab="K years ago", col=adjustcolor("cornflowerblue", alpha= 0.2), border=adjustcolor("cornflowerblue", alpha= 0.9), main="", add=TRUE)
}
```


I'm creating new rows for this table, combining dates in different ways to make the CDFs below look more authentic. This makes it so that pre-ag always happens before post-ag. What I've done is given the later date to the earlier date when those dates are missing. 
```{r}
h <- which(is.na(domestication_times[,3]))
domestication_times <- cbind(domestication_times, rep(NA, length(domestication_times[,1])))
domestication_times[,9] <- domestication_times[,3]
domestication_times[h,9] <- domestication_times[h,7]
colnames(domestication_times)[9] <- "adopt exploitation date"
domestication_times[,10] <- domestication_times[,7]
domestication_times[which(is.na(domestication_times[,10])),10] <- 0
colnames(domestication_times)[10] <- "start of ag"
#save(domestication_times, file="~/Desktop/Human density and the origins of agriculture/Domestication timing larson 2014.Rdata")
```



I think these are best described by a cummulative distribution, showing how they accumulate over time. 

```{r}
for(i in 1:8){
type_number <- i
	match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
	maxer <- max(match, na.rm=TRUE)
	j <- ecdf(maxer-match)
	print(levels(domestication_times$Region)[ type_number])
	print(match)
	print(j)
}
```



```{r}
par(mfcol=c(2,5), mar=c(4,0,5,0))

plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)
plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)

for(i in 1:8){
type_number <- i
	match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
	maxer <- max(match, na.rm=TRUE)
	j <- ecdf(maxer-match)
	#print(j)
	
plot(0,0, xlim=c(15,0), ylim=c(0,100), ylab="Percent of species that will eventually \n be domesticated in a region", xlab="Thousand years ago", main=levels(domestication_times$Region)[ type_number], type="n", yaxt="n")

x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- 100 * (c(0, j(seq(0, maxer, length.out=100))))

lines(x_seq, y_seq,  ylim=c(-1,1))
polygon(c(0, x_seq), c(0, y_seq), border=adjustcolor("cornflowerblue",alpha=1), col=adjustcolor("cornflowerblue", alpha=0.2))
if(i == 2 | i == 1)axis(2)

if(i == 3)mtext("Cummulative distribution function for the accumulation of domesticates", 3, line=3.8, col="cornflowerblue")
}


```


```{r}
par(mfcol=c(2,5), mar=c(4,0,5,0))

plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)

plot(0,0, type="n", xaxt="n", xlab="", bty="n")
mtext("Percent of species that will eventually \n be domesticated in a region", 2, line=-5, cex=0.5)

for(i in 1:8){
type_number <- i
	match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
	maxer <- max(match, na.rm=TRUE)
	j <- ecdf(maxer-match)
	#print(j)
	
plot(0,0, xlim=c(15,0), ylim=c(0,100), ylab="Percent of species that will eventually \n be domesticated in a region", xlab="Thousand years ago", main=levels(domestication_times$Region)[ type_number], type="n", yaxt="n")

x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- 100 * (c(0, j(seq(0, maxer, length.out=100))))

lines(x_seq, y_seq,  ylim=c(-1,1))
polygon(c(0, x_seq), c(0, y_seq), border=adjustcolor("cornflowerblue",alpha=1), col=adjustcolor("cornflowerblue", alpha=0.2))
abline(v= maxer - quantile(j)[2], col="limegreen", lwd=2)
if(i == 2 | i == 1)axis(2)
if(i == 2)mtext("25%", 3, line=3.5, adj=-1, col="limegreen")
if(i == 3)mtext("Cummulative distribution function for the accumulation of domesticates", 3, line=3.8, col="cornflowerblue")
if(i == 4)mtext("Choose a y to predict an x", 3, line=3.3, col="cornflowerblue")
	break_one <- maxer
			break_two <- maxer - quantile(j)[2]
				
	polygon(x=c(break_two, break_two, break_one, break_one), y=c(0, 1, 1, 0), col=adjustcolor("cornflowerblue", alpha=0.2), border=adjustcolor("cornflowerblue",alpha=1))
			lines(x=c(break_two, break_two), y=c(0,-1), col="cornflowerblue")
			abline(h = 25, col="limegreen", lwd=2)
}


```
Make this a function. 
There is a choice of two methods here. At the end of this section we need to print the desision we're passing to the later analyses. 






## Defining origins
![](Larson_origins.jpg)


```{r}
origins <- readShapePoly('Origins_updated.shp')

origin.time.region <- c(2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 
                        2, 2, 1, 2, 2, 2, 2, 2, 2, 2) # 1 = early; 2 = middle
as.character(origins$CONTINENT)

#subset_order <- c(1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 17, 18)
subset_order <- c(8, 10, 9, 5, 18, 7, 6, 20, 1, 2, 13, 16)
origins_subset <- origins[subset_order,]
origins_subset$CONTINENT
origins_subset$name

```

```{r}
library(maps)
map()
map(origins, add=TRUE, fill=TRUE, col=adjustcolor("cornflowerblue", alpha=1))

```


```{r}
map()
d <- readPNG("Larson_origins.png")
rasterImage(d, -180, -90, 180, 110, interpolate=TRUE, col=d)
map(add=TRUE)
map(origins, add=TRUE, fill=TRUE, col=adjustcolor("cornflowerblue", alpha=1))

# need to reproject
```
This is obviously a bad projection fit right now. 


##Import raster data
```{r}
#subset and reorder origins. This is currently done at the end of the plot but should be moved forward.

# Load data for population density
load("PopD_all_December.rdata")
PopD.ALL
```

```{r}
# Extract data to a matrix
Pop <- values(PopD.ALL)
r <- raster(PopD.ALL, 1)
r
```




## GAM smoothing models
#### Justification for General Adative Models.
  We need to justify our decision to use a GAM over other models. This should include citations to back up those arguments. 


### Fit and plot GAM model with different degrees of freedom
We should make our decisions very transparent here. We should be able to justify our decision of 3 degrees of freedom over other possible values. 

#### Density projections

```{r, cache=TRUE}
# Read the polygons
origins <- readShapePoly('Origins_updated.shp')
```


```{r}
# Extract data
per.origin <- extract(r, origins, cellnumber = TRUE, buffer = 100000)
names(per.origin) <- origins@data[, 1]

str(per.origin)
```

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))
for(h in 1:20){
#h <- 3
originI <- Pop[per.origin[[h]][, 1], ]
x_values <- matrix(c(4:21), dim(originI)[1], 18, byrow=TRUE)
x_value_vector <- as.vector(x_values)
y_value_vector <- scale(as.vector(originI))
density_trend <- cbind(x_value_vector, y_value_vector)
plot(density_trend, col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(-10,10), xlim=c(21,4))

points(density_trend, cex=0.5, col=adjustcolor("cornflowerblue", 0.5))

}
```

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))
for(h in 1:20){
#h <- 3
originI <- Pop[per.origin[[h]][, 1], ]
x_values <- matrix(c(4:21), dim(originI)[1], 18, byrow=TRUE)
x_value_vector <- as.vector(x_values)
y_value_vector <- scale(as.vector(originI))
density_trend <- cbind(x_value_vector, y_value_vector)
plot(density_trend, col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(-4,8), xlim=c(21,4))

points(density_trend, cex=0.5, col=adjustcolor("grey", 0.1))
gammer <- loess(density_trend[,2] ~ density_trend[,1] )
summary(gammer)
lines(density_trend[,1] ,predict(gammer),  col="cornflowerblue", lwd=2)



}




```

span	
the parameter α which controls the degree of smoothing.

The size of the neighbourhood is controlled by α (set by span or enp.target). For α < 1, the neighbourhood includes proportion α of the points, and these have tricubic weighting (proportional to (1 - (dist/maxdist)^3)^3). For α > 1, all points are used, with the ‘maximum distance’ assumed to be α^(1/p) times the actual maximum distance for p explanatory variables.

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))
for(h in 1:20){
#h <- 3
originI <- Pop[per.origin[[h]][, 1], ]
x_values <- matrix(c(4:21), dim(originI)[1], 18, byrow=TRUE)
x_value_vector <- as.vector(x_values)
y_value_vector <- scale(as.vector(originI))

density_trend <- cbind(x_value_vector, y_value_vector)

#points(density_trend, cex=0.5)
gammer <- loess(density_trend[,2] ~ density_trend[,1], span = .5)
summary(gammer)
predict_gam <- predict(gammer, se=TRUE)

plot(density_trend, col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(-1.35,1.35), xlim=c(21,4))


polygon(x=c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window), y=c(-2, 2, 2, -2), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x=c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window), y=c(-2, 2, 2, -2), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

abline(h=0, lty=2, col="grey")

lines(density_trend[,1] ,predict_gam$fit,  col="cornflowerblue")
lines(density_trend[,1] ,  predict_gam$fit + predict_gam$se.fit,  col="grey", lty=1)
lines(density_trend[,1] ,  predict_gam$fit - predict_gam$se.fit,  col="grey", lty=1)


}

```


```{r}
# need to add a global mean, an everything but the origins mean, and a buffer around the origins mean. 
# Function standardization
std <- function(x) {
  b <- (x - min(x)) / (max(x) - min(x))
  return(rev(b))
}


diff_df <- function(h){ 
# Calculating mean and 
global.means <- global.SD <- list()

for (j in 1:length(per.origin)) {
  #print(j)
  originI <- Pop[per.origin[[j]][, 1], ]
  time <- 21:4
  originI <- na.exclude(originI)
  b <- apply(originI, 1, std)
  nJ <- nrow(originI)
  predictions <- matrix(nrow = nJ, ncol = length(time))
  colnames(predictions) <- as.character(time)
  for(i in 1:nJ) {
    
    # Need to show a gradient of these df values. 
    model <- gam(b[, i] ~ s(time, df = h))
    col <- sample(rainbow(100), 1)
    predictions[i, ] <- predict(model)
  }
  global.means[[j]] <- apply(predictions, 2, mean) 
  global.SD[[j]] <- apply(predictions, 2, sd)
}


names(global.means) <- paste(names(per.origin), "Means")
names(global.SD) <- paste(names(per.origin), "SD")

return(list(global.means, global.SD))
}


```

```{r}
# Confirm that the x-axis is oriented correctly
for_3 <- diff_df(1)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

i <- 1
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,20))


polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

originI <- Pop[per.origin[[i]][, 1], ]
for(j in 1:18){
points(23- c(jitter(rep(4, length(originI[,j])), 4.5)  + j), originI[,j], pch=19, cex=.1)
}

polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]], type="b", pch=names(global.means[[i]]))

axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[1], 3, line=-2)

```


```{r}
means_matrix <- matrix(rep(NA,19*20), 20, 19)
colnames(means_matrix) <- c("origin", rev(seq(4, 21, by=1)))
means_matrix[,1] <- names(global.means)
for(i in 1:20){
means_matrix[i,2:19] <- global.means[[i]]
}
```

```{r}
kable(means_matrix, caption= "Mean values")
```


```{r}
#global.SD

SD_matrix <- matrix(rep(NA,19*20), 20, 19)
colnames(SD_matrix) <- c("origin", rev(seq(4, 21, by=1)))
SD_matrix[,1] <- names(global.SD)
for(i in 1:20){
SD_matrix[i,2:19] <- global.SD[[i]]
}
```

```{r}
kable(SD_matrix, caption= "SD values")
```


```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for(j in 1:20){
plot(means_matrix[1,2:19], col=adjustcolor("cornflowerblue", alpha=0.8), pch=names(means_matrix[1,2:19]), type="n", xlab="year", ylab="Density", xaxt="n", ylim=c(0,1))

originI <- Pop[per.origin[[j]][, 1], ]
for(h in 1:18){
points(23- c(jitter(rep(4, length(originI[,h])), 4.5)  + h), originI[,h], pch=19, cex=.1)
}
  
lines(means_matrix[j,2:19], col=adjustcolor("cornflowerblue", alpha=0.8), pch=names(means_matrix[j,2:19]), type="b", xlab="year", ylab="Density", xaxt="n")
}

axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))

```




```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(1)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
  

plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))  
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using one degree of freedom

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(2)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using two degree of freedom

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(3)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using three degree of freedom

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(4)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using four degree of freedom


```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(5)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))

polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using 5 degree of freedom

```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(10)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))  
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using 10 degree of freedom



```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(12)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))  
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using 12 degree of freedom




```{r}
par(mfrow=c(4,5), mar=c(0,0,0,0))

for_3 <- diff_df(17)
global.means <- for_3[[1]]
global.SD <- for_3[[2]]

for(i in 1:20){
plot(4:21, global.means[[i]], col=adjustcolor("cornflowerblue", alpha=0.8),  xlab="year", ylab="Density", xaxt="n", type="n", ylim=c(0,1), xlim=c(0,22), xaxt="n", yaxt="n")

polygon(x=22-c(Start_of_early_window, Start_of_early_window, End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("limegreen", alpha= 0.2), border=adjustcolor("limegreen", alpha= 0.9))

polygon(x= 22-c( End_of_early_window_start_of_late_window, End_of_early_window_start_of_late_window, End_of_late_window, End_of_late_window) , y=c(-1, 2, 2, -1), col=adjustcolor("firebrick", alpha= 0.2), border=adjustcolor("firebrick", alpha= 0.9))   
  
polygon(c(4:21,21:4) -3 , c(global.means[[i]] + abs(global.SD[[i]]), rev(global.means[[i]] - abs(global.SD[[i]]))), col="cornflowerblue")
lines(global.means[[i]])

#axis(1, at=seq(1,18, by=1), label=rev(seq(4, 21, by=1)))
mtext(names(global.means)[i], 3, line=-1, cex=.5, adj=.3)
}
```
GAM model using 17 degree of freedom



#### Productivity
```{r}
# Load patricks productivity PCA data
load('Productivity_ALL.RDATA')

# Load origin shapefiles
origins <- readShapePoly('Origins_updated.shp')

origin.time.region <- c(2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 
                        2, 2, 1, 2, 2, 2, 2, 2, 2, 2) # 1 = early; 2 = middle


# Extract the data
prod.origin <- extract(Productivity.ALL, origins)
# Mean and SD per region
means <- lapply(prod.origin, colMeans, na.rm = TRUE)
sds <- lapply(prod.origin, sd, na.rm = TRUE)
names(means) <- origins@data$CONTINENT
ymax <- max(unlist(means))
ymin <- min(unlist(means))
time <- 4:21

# Plot
#pdf("productivity.pdf", 20, 30) 
par(mfrow = c(5, 4), mar = c(2, 2, 2, 0))
for (i in 1:length(means)) {
  plot(y = means[[i]], x = time, xlim = c(21, 4), ylim = c(ymin, ymax),
       main = names(means)[i], cex.main = 1, cex.lab = 1, cex.axis = 1,
       ylab = "Productivity (PCA axis)", xlab = "Thousand of years ago (k)",
       pch = 20, lwd = 1, type = "l", 
       col = c("purple", "green")[origin.time.region[i]])
  up <- sds[[i]] + means[[i]]
  down <-  means[[i]] - sds[[i]]
  lines(up ~ time, lty = 2)
  lines(down ~ time, lty = 2)
  
}
#dev.off()
```




##Compare rates between origins and not-origins

##Compare rates between different time periods


##Setup final figure
#### Frame in the layout
```{r}
a <- layout(matrix(c(
	1, 1, 1, 1, 1, 1, 1, 1,
	3,	6, 7, 8, 9, 10, 11,	4, 
	3,	5, 5, 5, 5, 5, 5, 	4, 
	3, 	12, 13, 14, 15, 16, 17,	4,
	2, 2, 2, 2, 2, 2, 2, 2
	), 5, 8, byrow=TRUE), width=c(1, 1, 1, 1, 1, 1, 1, 1), height=c(0.5, 1, 1.5, 1, 0.5))
layout.show(a)
```

#### Make blank template plots
```{r}
frameplot <- function(){
	plot(21:0,rep(0, 22), xlim=c(17,4), ylim=c(0, 2.25), type="n", xaxt="n", yaxt="n", xlab="", ylab="")
}

frameplot_bottom <- function(){
	plot(21:0,rep(0, 22), xlim=c(17,4), ylim=c(-0.25, 2), type="n", xaxt="n", yaxt="n", xlab="", ylab="")
}
```

```{r}
frameplot()
frameplot_bottom()
```




##map for final figure



#### Make the map for the center panel (#5 on layout panel)

```{r}
d <- readPNG("earth.png")
```

![](earth.png)

```{r}
png(file=paste("40962.png",sep=""),width=2000,height=1000, bg="transparent")
par(mar=c(0,0,0,0))
plot(seq(-180, 180, length.out = 19), seq(-90, 90, length.out = 19), type="n",xlim=c(-180, 180),ylim=c(-90, 90), xaxt="n")

rasterImage(d, -180, -90, 180, 90, interpolate=TRUE, col=d)

polygon(x=c(-180,-180, 180,180), y=c(-90, 90, 90, -90), col=adjustcolor("white", alpha=0.1))
#rasterImage(d, -13.5, -13.5, 375, 375, interpolate=TRUE, col=d)
plot(origins_subset, add=TRUE, col=adjustcolor("white", alpha=.8), xaxt="n", border="white", lwd=4) #still need to reproject!!!
dev.off()
```

![](40962.png)




##Trend through time panel

#### Setup the plot template for small panel plots (#6-17 on layout panel)
```{r}
###################

type_number <- 8

complex_figure <- function(type_number, i, means, sds){
						
if(i < 6)	polygon(x=c(12,12,8.2,8.2), y=c(-1,3,3,-1), col=adjustcolor("cornflowerblue", alpha=0.4), border=NA)					
if(i > 5)	polygon(x=c(8.2,8.2,4.2,4.2), y=c(-1,3,3,-1), col=adjustcolor("limegreen", alpha=0.4), border=NA)
									
	match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 9]
	maxer <- max(match, na.rm=TRUE)
	j <- ecdf(maxer-match)
	print(j)
	

x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- -c(0, j(seq(0, maxer, length.out=100)))

#lines(x_seq, y_seq, type="l", ylim=c(-1,1))
#polygon(c(0, x_seq), c(0, y_seq), border="black", col=adjustcolor("cornflowerblue", alpha=0.5))
#abline(v= maxer - quantile(j)[2])

	
	break_one_1 <- maxer
			break_two_1 <- maxer - quantile(j)[2]
				
#	polygon(x=c(break_two_1, break_two_1, break_one_1, break_one_1), y=c(0, 1, 1, 0), col=adjustcolor("cornflowerblue", alpha=0.5), border=NA)
			

	match <- domestication_times[ which(domestication_times$Region == levels(domestication_times$Region)[ type_number]), 10]
	maxer <- max(match, na.rm=TRUE)
	j <- ecdf(maxer-match)
	print(j)
	

x_seq <- rev(c(0,seq(0, maxer, length.out=100)))
y_seq <- 2+c(0, j(seq(0, maxer, length.out=100)))

#lines(x_seq, y_seq)
#polygon(c(0, x_seq), c(2, y_seq), border="black", col=adjustcolor("limegreen", alpha=0.5))

	
	break_one_2 <- maxer
			break_two_2 <- maxer - quantile(j)[2]
				
#	polygon(x=c(break_two_2, break_two_2, break_one_2, break_one_2), y=c(1, 2, 2, 1), col=adjustcolor("limegreen", alpha=0.5), border=NA)
			
	
		#abline(v=11)
	type <- 1
		
		if(type == 1){
	x <- c(means[[i]] , means[[i]]  + abs(sds[[i]]), means[[i]]  - abs(sds[[i]]))
	scaled <- scale(x , center=FALSE)
	meanss <- scaled[1:18]
	sdss_plus <- scaled[19:36]
	sdss_minus <- scaled[37:54]
	#abline(v=10, col="red")
	length(scaled)
	#lines(4:21, means[[i]] + sds[[i]])
	#polygon(x=c(4:21, 21:4), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")
	polygon(x=c(21:4,4:21), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")	
	}
	
	if(type == 2){
	x <- c(means[[i]] , means[[i]]  + abs(sds[[i]]), means[[i]]  - abs(sds[[i]]))
	scaled <- x + 1 #scale(x , center=FALSE)
	meanss <- scaled[1:18]
	sdss_plus <- scaled[19:36]
	sdss_minus <- scaled[37:54]
	#abline(v=10, col="red")
	length(scaled)
	#lines(4:21, means[[i]] + sds[[i]])
	polygon(x=c(4:21, 21:4), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")	
	}

if(type == 3){
	x <- c(means[[i]] , means[[i]]  + abs(sds[[i]]), means[[i]]  - abs(sds[[i]]))
	scaled <- x #scale(x , center=FALSE)
	meanss <- scaled[1:18]
	sdss_plus <- scaled[19:36]
	sdss_minus <- scaled[37:54]
	#abline(v=10, col="red")
	length(scaled)
	#lines(4:21, means[[i]] + sds[[i]])
	polygon(x=c(4:21, 21:4), y=c(sdss_plus, rev(sdss_minus)), col=adjustcolor("firebrick", alpha=1), border="white")	
	}

	
	
means_long_y <- c(1,1,1,1,1, meanss)
means_long_x <- c(0:4, 4:21)
 
			break_one <- break_one_2
			break_two <- break_two_2
		#		polygon(x=c(break_one, break_one, 22, 22), y=c(1, 2, 2, 1), col=adjustcolor("white", alpha=0.8), border=NA)
		#		polygon(x=c(break_two, break_two, break_one, break_one), y=c(1, 2, 2, 1), col=adjustcolor("white", alpha=0), border=NA)
			#	polygon(x=c(-1,-1, break_two , break_two), y=c(1.9, 3.1, 3.1, 1.9), col=adjustcolor("white", alpha=0.8), border=NA)	
				#abline(v= break_one, col="white")
				#abline(v= break_two, col="white")
				
				break_one <- break_one_1
			break_two <- break_two_1
		#		polygon(x=c(break_one, break_one, 22, 22), y=c(0, 1, 1, 0), col=adjustcolor("white", alpha=0.8), border=NA)
		#		polygon(x=c(break_two, break_two, break_one, break_one), y=c(0, 1, 1, 0), col=adjustcolor("white", alpha=0), border=NA)
			#	polygon(x=c(-1,-1, break_two , break_two), y=c(-1.1, .1, .1, -1.1), col=adjustcolor("white", alpha=0.8), border=NA)	
				#abline(v= break_one, col="white")
				#abline(v= break_two, col="white")
				
#lines(x=c(break_one_2, break_one_2), y=c(1,3), col="white")
#lines(x=c(break_one_1, break_one_1), y=c(1,-1), col="white")
#lines(x=c(break_two_2, break_two_2), y=c(1,3), col="white")
#lines(x=c(break_two_1, break_two_1), y=c(1,-1), col="white") 
#lines(4:21, meanss)
	lines(21:4, meanss)
	
}


```

```{r}
frameplot()
complex_figure(7, 1, global.means, global.SD) 
axis(1)
axis(2)
```


##Assemble the figure
#### Assemble the figure
```{r}
quartz(width=8, height=8)

layout(matrix(c(
	1, 1, 1, 1, 1, 1, 1, 1,
	3,	6, 7, 8, 9, 10, 11,	4, 
	3,	5, 5, 5, 5, 5, 5, 	4, 
	3, 	12, 13, 14, 15, 16, 17,	4,
	2, 2, 2, 2, 2, 2, 2, 2
	), 5, 8, byrow=TRUE), width=c(1, 1, 1, 1, 1, 1, 1, 1), height=c(0.5, 1, 1.5, 1, 0.5))


par(mar=c(0,0,0,0))

# 1-4 label margins
blankplot <- function(){
	
	plot(0,0, xlim=c(4,21), ylim=c(1, 1.25), bty="n", type="n", xaxt="n", yaxt="n", xlab="", ylab="")
}

blankplot()
blankplot()
blankplot()
blankplot()





origins <- readShapePoly('Origins_updated.shp')

origin.time.region <- c(2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 
                        2, 2, 1, 2, 2, 2, 2, 2, 2, 2) # 1 = early; 2 = middle
as.character(origins$CONTINENT)

#subset_order <- c(1, 2, 3, 5, 6, 8, 9, 10, 11, 12, 17, 18)
subset_order <- c(8, 10, 9, 5, 18, 7, 6, 20, 1, 2, 13, 16)
origins_subset <- origins[subset_order,]
origins_subset$CONTINENT



d <- readPNG("earth.png")
png(file=paste("40962.png",sep=""),width=2000,height=1000, bg="transparent")
par(mar=c(0,0,0,0))
plot(seq(-180, 180, length.out = 19), seq(-90, 90, length.out = 19), type="n",xlim=c(-180, 180),ylim=c(-90, 90), xaxt="n")

rasterImage(d, -180, -90, 180, 90, interpolate=TRUE, col=d)

polygon(x=c(-180,-180, 180,180), y=c(-90, 90, 90, -90), col=adjustcolor("white", alpha=0.1))
#rasterImage(d, -13.5, -13.5, 375, 375, interpolate=TRUE, col=d)
plot(origins_subset, add=TRUE, col=adjustcolor("white", alpha=.8), xaxt="n", border="white", lwd=4) #still need to reproject!!!
dev.off()

d <- readPNG("40962.png")
dim(d)
par(mar=c(0,0,0,0))
plot(0:360,0:360,type="n",xlim=c(20,360),ylim=c(65,295), yaxt="n", xaxt="n")
rasterImage(d, -28.5, -13.5, 388, 375, interpolate=TRUE, col=d)
axis(2, label=seq(-90, 90, length.out = 19), at=seq(1, 360, length.out = 19), las=1)
mtext("latitude", 2, line=4, at=180)
abline(h=seq(1, 360, length.out = 19), col=adjustcolor("grey10", alpha= 0.4), lwd=1)
abline(h=180, col=adjustcolor("white", alpha= .5), lwd=1)


load('PopD_all_December.rdata')

# Extract the data
prod.origin <- extract(PopD.ALL, origins_subset)

library(matrixStats)
# Mean and SD per region
means <- lapply(prod.origin, colMeans, na.rm = TRUE)
sds <- lapply(prod.origin, colSds, na.rm = TRUE)

## new values from Bruno's GAM model (produced in script called Population_Trend_per_y.R)
means <- global.means
sds <- global.gams

names(means) <- origins_subset@data$CONTINENT
ymax <- max(unlist(means))
ymin <- min(unlist(means))
time <- 4:21
#plot(origins)
#means[[1]] +
#sds[[1]]
#scale(as.numeric(means[[1]]), center=FALSE)

name_vector <- as.character(origins_subset@data$CONTINENT)



for(i in 1:12){

	

	if(i > 6){frameplot()}else{frameplot_bottom()}

	
		## customize polygons for each graph
	if(i == 1){ #mesoamerica  #values from Larson
		
			complex_figure(3, i, means, sds)
				
	
		}
	
	
	#########
	if(i == 2 ){ #NW lowlands SA  #values from Larson
		
		complex_figure(6, i, means, sds)
	

		}
		
		#########
	if( i == 3){ #NW lowlands SA  #values from Larson
		
		complex_figure(6, i, means, sds)
		
		}


		#########
	if(i == 4){ #Fertile crescent aka Southwest asia  #values from Larson
		
		
	complex_figure(8, i, means, sds)
				
		}
		
		#########
	if(i == 5){ #loess plateau  #values from Larson
		
		complex_figure(2, i, means, sds)
			
		}
		
		
		#########
	if(i == 6){ #new guinea  #values from Larson
		
		complex_figure(4, i, means, sds)
		
		}


#########
	if(i == 7){ #Eastern N.A.  #values from Larson
		
		complex_figure(5, i, means, sds)
		
			}


		#########
	if(i == 8){ #Andes  #values from Larson
		
		complex_figure(6, i, means, sds)
		
				}


#########
	if(i == 9){ #W. African Sav  #values from Larson
		
		complex_figure(1, i, means, sds)
		
			}


#########
	if(i == 10){ #Sudanic sav  #values from Larson
		
		complex_figure(1, i, means, sds)
		
				}


#########
	if(i == 11){ #Ganges  #values from Larson
		
		
		complex_figure(7, i, means, sds) 
		
		}


#########
	if(i == 12){ #loess  #values from Larson
		
		complex_figure(2, i, means, sds)
		 
		 		}

		
		
		#lines(4:21, means[[i]])
		
		abline(h = 1, col=adjustcolor("forestgreen", alpha=.5), lty=2)
		
	# add axes to some locations
	if(i == 1 | i == 7){axis(2, at=seq(0,2, by=0.25), label=seq(0,2, by=0.25), las=1)}
	if(i == 6 | i == 12){axis(4, at=seq(0,2, by=0.25), label=seq(0,2, by=0.25), las=1)}
	#if(i == 6 | i == 12){axis(4, at=seq(2,3, by=0.25), label=seq(0,1, by=0.25), las=1)
	#	axis(4, at=seq(-1,0, by=0.25), label=rev(seq(0,1, by=0.25)), las=1)
	#	}
	if(i > 6){axis(1)} else{axis(3)}

	
	# add text 
	if(i < 7){polygon(x=c(-30, -30, 30, 30), y=c(-0.1, -0.5, -0.5, -0.1), col="black")
	mtext(name_vector[i], 1, line=-1.2, col="white", cex=0.5)}
	
	if(i > 6){polygon(x=c(-30, -30, 30, 30), y=c(2.1, 2.5, 2.5, 2.1), col="black")
	mtext(name_vector[i], 3, line=-1.2, col="white", cex=0.5)}
	
	# add axis labels
	if(i == 1 | i ==  7){mtext("scaled density potential", 2, line=4, at=1)}
	if(i ==  3){mtext("Thousand years before present", 3, line=3.5, at =5)}
	if(i ==  9){mtext("Thousand years before present", 1, line=3.5, at =5)
		
		}
	
}






saveToPDF <- function(...) {
    d = dev.copy(pdf,...)
    dev.off(d)
}

saveToPNG <- function(...) {
    d = dev.copy(png,...)
    dev.off(d)
}

## Try them out

saveToPDF("my.pdf", height=8,width=8)
saveToPNG("my.png", height=8, width=8, units="in", res=300)
dev.off()



```

